transmitted through a Metal of a Current in the Metal. 387 
units, v being 3.10 10 , so a = ^ ^ 20 ; X is in these units the same 
as in the electromagnetic system. If P' is in volts P' = 3.1 0 2 P, 
P being in electrostatic units ; if a" is in ohms a' = 10 9 <t", so that 
the change of phase is, when the quantities are in the ordinary 
practical units, dropping the dashes, 
A _ 
3 . 10 9 -t — — P sin S cos Sr. 
47 t-<7 
The Hall coefficient C is related to X by the equation 
The change of phase is therefore 
_3_ 
4tt 2 
ACt 
P sin S cos ^ 
P being in volts, a in ohms, and C in electromagnetic units as 
given by Hall. 
Now — is the current per unit area of the metal in amperes. 
<j 
If we have a metallic mirror 1 centimetre broad and t centi- 
metres thick with a current G flowing through it, then 
P = G 
a t 
G being in amperes. 
The change of phase is therefore 
_ 3 ^ 
47 r 2 
ACt 
ter 
G sin S cos S'. 
If we take the case of Bismuth which has a large Hall 
coefficient, viz. 8’58.10~ 6 , and for which cr — T4.10 -4 , we get the 
change of phase 
if A y G 10~ 2 sin S cos S, 
7 r 2 t 
which as A is less than 1, and r is 2.10 -15 for yellow light, is 
a quantity too small for any measurement since G cannot be 
made very large for a thin film of metal. 
For light polarised perpendicularly to the plane of incidence, 
this plane containing the direction of the current, we have the 
ratio of the reflected wave’s amplitude to that of the incident 
wave 
an — v 
an + v' 
VOL. XI. PT. V. 
28 
